Orbit optimization for ASTROD-GW and its time delay interferometry with two arms using CGC ephemeris

ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitation Wave detection) is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared to that of LISA. The mission orbits of the 3 spacecraft forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4 and L5. The 3 spacecraft range interferometrically with one another with arm length about 260 million kilometers. In order to attain the requisite sensitivity for ASTROD-GW, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. For suppressing laser frequency noise, we need to use time delay interferometry (TDI) to match the two different optical paths (times of travel). Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the (TDI), we simulate the time delay numerically using CGC 2.7 ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the residual optical path differences in the first and second generation TDI for one-detector case. In our optimized mission orbits for 20 years, changes of arm length are less than 0.0003 AU; the relative Doppler velocities are less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.Comment: 17 pages, 7 figures, 1 tabl

Numerical simulation of time delay interferometry for eLISA/NGO

eLISA/NGO is a new gravitational wave detection proposal with arm length of 10^6 km and one interferometer down-scaled from LISA. Just like LISA and ASTROD-GW, in order to attain the requisite sensitivity for eLISA/NGO, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise etc. In previous papers, we have performed the numerical simulation of the time delay interferometry (TDI) for LISA and ASTROD-GW with one arm dysfunctional by using the CGC 2.7 ephemeris. The results are well below their respective limits which the laser frequency noise is required to be suppressed. In this paper, we follow the same procedure to simulate the time delay interferometry numerically. To do this, we work out a set of 1000-day optimized mission orbits of the eLISA/NGO spacecraft starting at January 1st, 2021 using the CGC 2.7 ephemeris framework. We then use the numerical method to calculate the residual optical path differences in the second-generation TDI solutions as in our previous papers. The maximum path length difference, for all configurations calculated, is below 13 mm (43 ps). It is well below the limit which the laser frequency noise is required to be suppressed for eLISA/NGO. We compare and discuss the resulting differences due to the different arm lengths for various mission proposals -- eLISA/NGO, an NGO-LISA-type mission with a nominal arm length of 2 x 10^6 km, LISA and ASTROD-GW.Comment: 17 pages, 13 figures, 3 tables, minor changes in description to match the accepted version of Classical and Quantum Gravity. arXiv admin note: text overlap with arXiv:1102.496